Understanding multipartite entanglement in systems of few particles

Whereas bipartite entanglement of pure states is well understood, multipartite entanglement is much more subtle. For instance, in the bipartite case there exists a unique maximally entangled state (MES) (in the sense that it cannot be obtained from any other state by deterministic local operations and classical communication (LOCC)), while in the multipartite case there are infinitely many. In fact, our understanding of the nonlocal properties of many-body states is far from complete even in the simplest case of just three subsystems. In this talk, we characterize the entanglement contained in a pure 3–qubit state via operational entanglement measures. To this end we derive a new decomposition for arbitrary 3–qubit states, which is characterized by five parameters (up to local unitary operations). We show that these parameters are uniquely determined by bipartite entanglement measures. These quantities, which are easily computable, characterize the different forms of bipartite entanglement required to generate the state following a particular preparation procedure and, hence, have a clear physical meaning. In addition to this, we show that the classification of states obtained in this way is strongly related to the one obtained when considering LOCC and that MES can be characterized by a simple condition in terms of our parameters. Moreover, our insights can be used to devise protocols in which a provider remotely prepares arbitrary (maximally) entangled states for spatially separated parties. These protocols are shown to efficient in terms of the quantum and classical communication that needs to be used to achieve them.